Finite Group Databasebeta

← #7658928

Subgroups — #7658928

Order 512.

4246 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42226C214yesmaximal, complemented
2#42054C214yesmaximal, complemented
3#42022C214yesmaximal, complemented
4#41667C214yesmaximal, complemented
5#41657C214yesmaximal, complemented
6#40995C214yesmaximal, complemented
7#40981C214yesmaximal, complemented
8#40671C214yesmaximal, complemented
9#40665C214yesmaximal, complemented
10#37613C211yesmaximal, characteristic, complemented
11#37610C211yesmaximal, characteristic, complemented
12#37608C211yesmaximal, characteristic
13#37600C212yesmaximal, complemented
14#37600C212yesmaximal, complemented
15#37555C212yesmaximal, complemented
16#36701C211yesmaximal, characteristic, complemented
17#36695C211yesmaximal, characteristic, complemented
18C2×#2845C211yesmaximal, characteristic, complemented
19#35951C214yesmaximal, complemented
20#35861C214yesmaximal, complemented
21#35809C214yesmaximal, complemented
22#34229C212yesmaximal, complemented
23#34215C211yesmaximal, characteristic, complemented
24C2×#533C2211yescharacteristic
25C2×#529C2212yes—
26#2845C2214yes—
27#2845C2214yes—
28#2845C2214yes—
29#2845C2211yescharacteristic
30#2845C2212yes—
31#2845C2211yescharacteristic
32#2839C2214yes—
33#2839C2214yes—
34#2839C2214yes—
35#2837C2214yes—
36#2831C2214yes—
37#2829C2214yes—
38#2822C2212yes—
39#2822C2211yescharacteristic
40#2822C2212yes—
41#2820C2212yes—
42#2820C2212yes—
43#2820C2212yes—
44#2819C2211yescharacteristic
45#2791C2214yes—
46#2790C2214yes—
47#2783C2214yes—
48#2781C2214yes—
49#2772C2214yes—
50#2770C2214yes—
51#2769C2214yes—
52#2767C2214yes—
53#2764C2214yes—
54#2762C2214yes—
55#2755C2214yes—
56#2754C2214yes—
57#2746C2214yes—
58#2744C2214yes—
59#2744C2214yes—
60#2741C2214yes—
61#2722C2214yes—
62#2721C2214yes—
63#2719C2214yes—
64#2718C2214yes—
65#2704C2214yes—
66#2702C2214yes—
67#2689C2214yes—
68#2687C2214yes—
69#2667C2214yes—
70#2667C2214yes—
71#2666C2214yes—
72#2666C2214yes—
73#2664C2214yes—
74#2664C2214yes—
75#2659C2214yes—
76#2655C2214yes—
77#2655C2214yes—
78#2655C2214yes—
79#2654C2214yes—
80#2654C2214yes—
81#2652C2214yes—
82#2652C2214yes—
83#2651C2214yes—
84#2651C2214yes—
85#2651C2214yes—
86#2639C2214yes—
87#2637C2214yes—
88#2637C2214yes—
89#2637C2214yes—
90#2637C2214yes—
91#2636C2214yes—
92#2630C2214yes—
93#2628C2214yes—
94#2621C2214yes—
95#2618C2214yes—
96#2612C2214yes—
97#2609C2214yes—
98#2606C2214yes—
99#2594C2214yes—
100#2593C2214yes—
101#2591C2214yes—
102#2589C2214yes—
103#2587C2214yes—
104#2585C2214yes—
105#2585C2214yes—
106#2585C2214yes—
107#2585C2214yes—
108#2585C2214yes—
109#2581C2214yes—
110#2579C2214yes—
111#2574C2214yes—
112#2569C2214yes—
113#2569C2214yes—
114#2564C2214yes—
115#2560C2214yes—
116#2556C2214yes—
117#2554C2214yes—
118#2553C2214yes—
119#2543C2214yes—
120#2536C2214yes—
121#2532C2214yes—
122#2531C2214yes—
123#2529C2214yes—
124#2529C2214yes—
125#2525C2214yes—
126#2525C2214yes—
127#2524C2214yes—
128#2522C2214yes—
129#2522C2214yes—
130#2522C2214yes—
131#2520C2214yes—
132#2519C2214yes—
133#2519C2214yes—
134#2515C2214yes—
135#2515C2214yes—
136#2510C2214yes—
137#2498C2214yes—
138#2498C2214yes—
139#2487C2214yes—
140#2481C2214yes—
141#2481C2214yes—
142#2481C2214yes—
143#2478C2214yes—
144#2475C2214yes—
145#2468C2214yes—
146#2468C2214yes—
147#2468C2214yes—
148#2462C2214yes—
149#2462C2214yes—
150#2450C2214yes—
151#2444C2214yes—
152#2443C2214yes—
153#2442C2214yes—
154#2442C2214yes—
155#2438C2214yes—
156#2419C2214yes—
157#2417C2214yes—
158#2417C2214yes—
159#2402C2214yes—
160#2402C2214yes—
161#2402C2214yes—
162#2396C2214yes—
163#2395C2214yes—
164#2392C2214yes—
165C2×#398C2214yes—
166C2×#398C2214yes—
167C2×#398C2214yes—
168#2368C2214yes—
169#2368C2214yes—
170#2361C2212yes—
171#2361C2214yes—
172#2361C2212yes—
173#2360C2212yes—
174#2360C2212yes—
175#2359C2214yes—
176#2359C2214yes—
177#2357C2212yes—
178#2356C2212yes—
179#2355C2214yes—
180#2355C2214yes—
181#2353C2214yes—
182#2352C2214yes—
183#2351C2212yes—
184#2349C2212yes—
185#2346C2214yes—
186#2345C2214yes—
187#2343C2214yes—
188#2334C2214yes—
189#2334C2214yes—
190#2331C2212yes—
191#2331C2212yes—
192#2318C2214yes—
193#2317C2212yes—
194C4×#125C2211yescharacteristic
195C4×#125C2211yescharacteristic
196C4×#125C2212yes—
197C4×#125C2211yescharacteristic
198C4×#125C2211yescharacteristic
199C4×#125C2212yes—
200C4×#124C2212yes—
201C4×#124C2212yes—
202C2×#382C2211yescharacteristic
203C2×#382C2212yes—
204#2275C2214yes—
205#2274C2212yes—
206C4×#117C2211yescharacteristic
207#533—28no—
208C2×C4⋊Q8C2312yes—
209#529—216no—
210C2×#126C2314yes—
211C2×#126C2314yes—
212C2×#126C2314yes—
213C2×#126C2314yes—
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#125C2312yes—
217C2×#125C2314yes—
218C2×#125C2314yes—
219C2×#124C2312yes—
220C2×#123C2314yes—
221C2×#123C2314yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×#121C2312yes—
227C2×#121C2314yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2314yes—
239C2×#117C2312yes—
240C2×#117C2314yes—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2314yes—
244C22×C4⋊C4C2312yes—
245C22×C4⋊C4C2314yes—
246C22×C4⋊C4C2314yes—
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2314yes—
250C22×C42C2311yescharacteristic
251#401C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#399C2314yes—
276#399C2314yes—
277#399C2314yes—
278#399C2314yes—
279#399C2314yes—
280#399C2314yes—
281#398C2314yes—
282#398C2314yes—
283#398C2314yes—
284#398C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#393C2314yes—
368#393C2314yes—
369#393C2314yes—
370#392C2314yes—
371#391C2314yes—
372#391C2312yes—
373#391C2312yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2314yes—
379#390C2314yes—
380#390C2312yes—
381#390C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2312yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#386C2314yes—
482#386C2314yes—
483#386C2314yes—
484#386C2314yes—
485#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#385C2314yes—
493#385C2314yes—
494#385C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2314yes—
498#385C2314yes—
499#385C2314yes—
500#385C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#384C2314yes—
508#383C2314yes—
509#383C2314yes—
510#383C2314yes—
511#382C2311yescharacteristic
512#382C2311yescharacteristic
513#382C2312yes—
514#382C2312yes—
515#382C2314yes—
516#382C2314yes—
517#382C2314yes—
518#382C2314yes—
519#382C2312yes—
520#382C2314yes—
521#382C2312yes—
522#382C2312yes—
523#382C2314yes—
524#382C2314yes—
525#382C2314yes—
526#381C2314yes—
527#381C2314yes—
528#381C2314yes—
529#380C2314yes—
530#380C2314yes—
531#380C2314yes—
532#380C2314yes—
533#380C2314yes—
534#380C2314yes—
535#380C2314yes—
536#380C2314yes—
537#380C2314yes—
538#380C2314yes—
539#380C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2314yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2312yes—
546C4×C4⋊C4C2312yes—
547C4×C4⋊C4C2312yes—
548C4×C4⋊C4C2312yes—
549C4×C4⋊C4C2314yes—
550C4×C4⋊C4C2314yes—
551C4×C4⋊C4C2314yes—
552C4×C4⋊C4C2314yes—
553C4×C4⋊C4C2312yes—
554C4×C4⋊C4C2312yes—
555C4×C4⋊C4C2312yes—
556C4×C4⋊C4C2312yes—
557C4×C4⋊C4C2314yes—
558C4×C4⋊C4C2314yes—
559C4×C4⋊C4C2314yes—
560C4×C4⋊C4C2312yes—
561C4×C4⋊C4C2312yes—
562C4×C4⋊C4C2314yes—
563C4×C4⋊C4C2314yes—
564C4×C4⋊C4C2314yes—
565C4×C22⋊C4C2314yes—
566C4×C22⋊C4C2314yes—
567C4×C22⋊C4C2314yes—
568C4×C22⋊C4C2312yes—
569C4×C22⋊C4C2314yes—
570C4×C22⋊C4C2314yes—
571C4×C22⋊C4C2314yes—
572C4×C22⋊C4C2314yes—
573C4×C22⋊C4C2314yes—
574C4×C22⋊C4C2314yes—
575C4×C22⋊C4C2314yes—
576C4×C22⋊C4C2312yes—
577#376C2311yescharacteristic
578#376C2311yescharacteristic
579#376C2314yes—
580#376C2314yes—
581C2×#95C2314yes—
582C2×#95C2314yes—
583C2×#95C2314yes—
584C2×#95C2314yes—
585C2×#95C2314yes—
586C43C2311yescharacteristic
587C43C2311yescharacteristic
588C22×Q8C2412yes—
589C22×Q8C2414yes—
590C22×D4C2414yes—
591C22×D4C2412yes—
592C22×D4C2414yes—
593C23×C4C2411yescharacteristic
594C23×C4C2414yes—
595C23×C4C2414yes—
596C23×C4C2414yes—
597C23×C4C2414yes—
598C23×C4C2414yes—
599C23×C4C2414yes—
600C23×C4C2412yes—
601C4⋊Q8—28no—
602#126—216no—
603#126—84no—
604#126—84no—
605#126—84no—
606#125—28no—
607#125—24no—
608#125—24no—
609#125—84no—
610#125—84no—
611#124—28no—
612#123—216no—
613#123—84no—
614C22⋊Q8—28no—
615C22⋊Q8—216no—
616C22⋊Q8—84no—
617C22⋊Q8—84no—
618#121—28no—
619#121—48no—
620C4×Q8—28no—
621C4×Q8—216no—
622C4×Q8—82no—
623C4×Q8—82no—
624C4×D4—216no—
625C4×D4—216no—
626C4×D4—28no—
627C4×D4—48no—
628C4×D4—84no—
629C4×D4—82no—
630C4×D4—82no—
631#117—28no—
632#117—24no—
633#117—216no—
634#117—42no—
635#117—84no—
636C2×C4⋊C4—44no—
637C2×C4⋊C4—48no—
638C2×C4⋊C4—84no—
639C2×C4⋊C4—82no—
640C2×C4⋊C4—82no—
641C2×C4⋊C4—84no—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C22⋊C4C2412yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2411yescharacteristic
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2411yescharacteristic
727C2×C42#4118yes—
728C2×C42C2414yes—
729C2×C42C2414yes—
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2414yes—
733C2×C42C2414yes—
734C2×C42C2414yes—
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2412yes—
738C2×C42C2412yes—
739C2×C42C2414yes—
740C2×C42C2414yes—
741C2×C42C2414yes—
742C2×C42C2414yes—
743C2×C42C2412yes—
744C2×C42C2412yes—
745C2×C42C2414yes—
746C2×C42C2414yes—
747C2×C42C2414yes—
748C2×C42C2411yescharacteristic
749C2×C42C2412yes—
750C2×C42C2411yescharacteristic
751#95C2412yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2412yes—
771#95C2414yes—
772#95C2414yes—
773#95C2412yes—
774#95C2412yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813C24C2514yes—
814C24C2511yescharacteristic
815C2×Q8—24no—
816C2×Q8—28no—
817C2×Q8—42no—
818C2×Q8—42no—
819C2×Q8—44no—
820C2×Q8—44no—
821C2×D4—28no—
822C2×D4—28no—
823C2×D4—28no—
824C2×D4—24no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—44no—
828C2×D4—44no—
829C2×D4—44no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—28no—
833C22×C4—28no—
834C22×C4—28no—
835C22×C4—28no—
836C22×C4—28no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4C2×#4114yes—
853C22×C4C2×#4118yes—
854C22×C4C2511yescharacteristic
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2514yes—
858C22×C4C2514yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2514yes—
862C22×C4C2514yes—
863C22×C4C2514yes—
864C22×C4C2514yes—
865C22×C4C2514yes—
866C22×C4C2514yes—
867C22×C4C2511yescharacteristic
868C22×C4C2512yes—
869C22×C4C2512yes—
870C22×C4C2511yescharacteristic
871C22×C4C2511yescharacteristic
872C22×C4C2512yes—
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—28no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—28no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—44no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—42no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—22no—
934C22⋊C4—24no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C42−1+414yes—
960C42—28no—
961C42—28no—
962C42—22no—
963C42—22no—
964C42—28no—
965C42—42no—
966C42—44no—
967C42—44no—
968C42—42no—
969C42—44no—
970C42—41no—
971C42—41no—
972C42—44no—
973C42—44no—
974C42—44no—
975C42—42no—
976C42—42no—
977C42—44no—
978C42—44no—
979C42—44no—
980C42C2×#4114yes—
981C42C2×#4118yes—
982C42C2×#4114yes—
983C23—22no—
984C23—22no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23C22×#4112yes—
993C23C2×2−1+412yes—
994C23#58512yes—
995C23C2611yescharacteristic
996Q8—48no—
997Q8—88no—
998D4—48no—
999D4—416no—
1000D4—88no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—28no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—48no—
1056C2×C4—88no—
1057C2×C4—88no—
1058C2×C4—88no—
1059C2×C4—88no—
1060C2×C4—88no—
1061C2×C4—164no—
1062C2×C4C22×#4112yes—
1063C2×C4C22×#4114yes—
1064C2×C4C22×#4112yes—
1065C2×C4C22×#4114yes—
1066C2×C4C2×2−1+412yes—
1067C2×C4C2×2−1+412yes—
1068C22—24no—
1069C22—22no—
1070C22—22no—
1071C22—24no—
1072C22—44no—
1073C22—44no—
1074C22—44no—
1075C22—44no—
1076C22—44no—
1077C22—44no—
1078C22—44no—
1079C22#346114yes—
1080C22C23×#4111yescharacteristic
1081C22C22×2−1+411yescharacteristic
1082C22C2×#58511yescharacteristic
1083C22H(7,𝔽2)12yes—
1084C222−1+612yes—
1085C4—22no—
1086C4—22no—
1087C4—24no—
1088C4—24no—
1089C4—22no—
1090C4—22no—
1091C4—42no—
1092C4—44no—
1093C4—44no—
1094C4—44no—
1095C4—44no—
1096C4—42no—
1097C4—41no—
1098C4—44no—
1099C4—44no—
1100C4—41no—
1101C4—44no—
1102C4—44no—
1103C4—44no—
1104C4—44no—
1105C4—44no—
1106C2—24no—
1107C2—84no—
1108C2C2×#346111yescharacteristic
1109C2#6285612yes—
1110C2#6305012yes—
1111C2#6305411yescharacteristic
1112C2#6306711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37608C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #42226C2semidirect
2. #42054C2semidirect
3. #42022C2semidirect
4. #41667C2semidirect
5. #41657C2semidirect
6. #40995C2semidirect
7. #40981C2semidirect
8. #40671C2semidirect
9. #40665C2semidirect
10. #37613C2semidirect
11. #37610C2semidirect
13. #37600C2semidirect
14. #37600C2semidirect
15. #37555C2semidirect
16. #36701C2semidirect
17. #36695C2semidirect
18. C2×#2845C2semidirect
19. #35951C2semidirect
20. #35861C2semidirect
21. #35809C2semidirect
22. #34229C2semidirect
23. #34215C2semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#422262
#420542
#420222
#416672
#416572
#409952
#409812
#406712
#406652
#376132
#376102
#376082
#376002
#375552
#367012
#366952
C2×#28452
#359512
#358612
#358092
#342292
#342152